Integral (Power Rule) Calculator Formula
Understand the math behind the integral (power rule) calculator. Each variable explained with a worked example.
Formulas Used
New Coeff
new_coeff = n != -1 ? coeff / (n + 1) : 0New Exp
new_exp = n + 1Definite
definite = n != -1 ? (coeff / (n + 1)) * (pow(upper, n + 1) - pow(lower, n + 1)) : 0Variables
| Variable | Description | Default |
|---|---|---|
coeff | Coefficient (a) | 6 |
n | Exponent (n) | 2 |
lower | Lower Bound | 0 |
upper | Upper Bound | 3 |
How It Works
Power Rule for Integration
Rule
integral of ax^n dx = (a/(n+1)) × x^(n+1) + C (when n ≠ -1)
For n = -1, the integral is a × ln|x| + C.
Definite Integral
Evaluate the antiderivative at the upper and lower bounds and subtract:
F(upper) - F(lower)
Worked Example
Integrate 6x² from 0 to 3.
coeff = 6n = 2lower = 0upper = 3
- 01Antiderivative: (6/3)x³ = 2x³
- 02F(3) = 2 × 27 = 54
- 03F(0) = 2 × 0 = 0
- 04Definite integral = 54 - 0 = 54
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